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Papoulis A. — The Fourier Integral and Its Applications
Papoulis A. — The Fourier Integral and Its Applications

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Название: The Fourier Integral and Its Applications

Автор: Papoulis A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 164

Добавлена в каталог: 24.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
All-pass filter      97
All-pass filter, ideal      109
All-pass filter, rational      117
Amplitude distortion      95—108 (see also Filters)
Analytic functions      283—311
Analytic properties of causal transforms      214
Analyzer      (see Spectrum analyzer)
Angelo, E. J., Jr.      124
Asymptotic forms, central-limit theorem      227
Asymptotic forms, Laplace      302
Asymptotic forms, lattice form of      230
Asymptotic forms, saddle-point      302—307
Asymptotic forms, stationary phase      139—143
Asymptotic slope      (see Signal-front delay)
Autocorrelation, derivatives      251
Autocorrelation, finite energy signals      242
Autocorrelation, finite power signals      245
Autocorrelation, periodic      250
Autocorrelation, pulse train      249
Band-limited interpolation      52 161
Band-limited signals, optimal      67
Band-limited signals, sampling theorem      50
Bandwidth, dynamic      159
Bernoulli theorem      232
Bessel functions      115
Bessel functions, asymptotic forms      142 305
Bessel functions, transform of      184
Beta density      238
Binomial distribution      50
Binomial filter      101
Blackman, R. B.      145
Bochner, S.      9
Bochner’s theorem      225
Bode, H. W.      192
Bounded variation      9
Bounds on a signal      34
Br (Bromwich path)      175
Branch points      288 298
Branch-cut line      288
Bremmer, H.      187
Butterworth filter with linear phase      105
Butterworth filter, causal      108
Butterworth filter, energy of      219
Calculus of residues      (see Residues)
Cauchy principal value      9
Cauchy — Riemann conditions      285
Cauchyв’s formula      295
Cauchyв’s integral theorem      292
Cauer, W.      307
Causal form of central-limit theorem      234
Causal functions      13
Causal functions, evaluation of      56
Causal systems      85
Causal transforms      195—217
Causal transforms, analyticity of      214
Causality conditions      213—217
Central-limit theorem      227—239
Central-limit theorem for time-limited signals      238
Central-limit theorem, causal form      234
Central-limit theorem, error correction      233 236
Central-limit theorem, lattice form      229
Chalk, J. H. H.      74
Characteristic functions      224
Characteristic functions, density      235
Churchill, R. V.      169
Complex integration      290
Conformality      285
Conjugate functions      16
Continuity      284
Continuity of autocorrelation      266
Convolution      26
Convolution and correlation      247
Convolution theorem, frequency      27
Convolution theorem, time      26
Convolution, evaluation of      59
Convolution, repeated      226
Copson, E. J.      140
Correlation      242—254 (see also Autocorrelation)
Corrington, M. S.      105
Cross-correlation, finite energy signals      244
Cross-correlation, finite power signals      252
Cross-correlation, periodic      254
Cross-energy spectrum      28 244
Cross-power spectrum      252
Davenport, W. B., Jr.      240
De Bruijn, N. G.      302
Delay time      96
Delay, group      113 135
Delay, phase      135
Delay, signal-front      135 187
Delta function      273—281
Delta function as a limit      279
Delta function, convolution of      275
Delta function, derivative of      274
Delta function, finite integral of      275
Delta function, transform of      36
Delta function, zero division of      39
density      223
Density, beta      238
Density, lattice      224
Detection      162
Differentiation, frequency      16
Differentiation, of autocorrelation      251
Differentiation, time      16
Discontinuities      9 30
dispersion      18 226 230
Distortion, amplitude      95—108
Distortion, phase      108—116
Distributions      270—281
Distributions, as generalized limits      278
Distributions, derivatives of      273
Distributions, physical concepts as      281
Distributions, properties of      272
Doetsch, G.      169
Duration of a signal, RMS      62
Duration of a signal, time-limited      66
Duration of a signal, with linear phase      64
Dynamic bandwidth      159
Echos      101 103
Eigenfunctions      68 83
Eigenfunctions for maximum energy      68—74
Eigenfunctions of linear systems      83
Eigenvalues      68 84
Energy of a signal      212
Energy spectrum      28
Energy theorem      27 194
Energy, finite, signals with      241—245
Erdelyi, A.      302
Error function      72 104
Even functions      11
Even functions, bilateral transforms of      190
Even-odd decomposition      12
Exponential, transform of      23
Extremum theorem      286
Fejer kernel      31
Fejer sum      46
Felsen, L. B.      302
Filters      94—136
Filters causal, with linear phase      106—108
Filters in-phase      132
Filters, all-pass      (see All-pass filter)
Filters, bandpass      120—136
Filters, bandpass transformation      122 127
Filters, binomial      101
Filters, Butterworth      (see Butterworth filter)
Filters, cosine      101
Filters, equivalent low-pass      122 132
Filters, gaussian      104
Filters, high-pass      100
Filters, ideal      97
Filters, low-pass      94—119
Filters, low-pass, general      103
Filters, modulated input      127 133
Filters, narrow-band      126
Filters, pulse-forming      116 (see also Phase distortion)
Filters, quadrature      132
Filters, symmetrical      120——131
Filters, unsymmetrical      131—134
Fourier integral, causal      13
Fourier integral, even      11
Fourier integral, imaginary      11
Fourier integral, kernel      18 30
Fourier integral, numerical techniques      53—59
Fourier integral, odd      11
Fourier integral, proof of      29
Fourier integral, real      11
Fourier integral, special forms      10—13
Fourier series      42—47
Fourier series, kernel      44
Fourier transform, generalized      259 261
Fourier transform, running      148 (see also Fourier integral)
Frequency modulation      165
Frequency shifting      162
Fresnel integrals      164 165 218
Friedman, B.      269
Functional      270 (see also Distributions)
Gain-bandwidth theorem      218
Gamma function      171 220
Gaussian filters      104
Gaussian function in central limit      224
Gaussian function, transform of      24
Generalized derivatives      276
Generalized Fourier transform      259 261
Generalized functions      270
Generalized harmonic analysis      259—264
Generalized harmonic analysis and power spectrum      261
Gibbs’ phenomenon      30
Gnedenko, B. V.      227
Goldman, S.      127
Group delay      134
Group delay, Fourier expansion of      113
Group velocity      139
Guillemin, E. A.      14
Halperin, I.      259
Harmonic analysis      259—264
Hermite polynomials in central limit      233
Hermite polynomials, transform of      78
High-pass filter      100
Hilbert transforms      198—212
Hurwitz polynomials      195 205
Hurwitz polynomials from biquadratic factors      206
Ideal filter, all-pass      109
Ideal filter, bandpass      123
Ideal filter, low-pass      97
Impulse function      269—282 (see also Delta function)
Impulse response of linear systems to      82
In-phase filter      132
Initial-value theorem      186
Input      81
Input wide-band      128 133
Input, modulated      127—134
Input, narrow-band      127 133
Instantaneous power spectrum      149
Integral equation      68
Integral theorems      192—218
Integration, complex      290
Interpolation, bard-limited      52 161
Inversion formula, evaluation of      56
Inversion formula, Fourier      7
Inversion formula, proof of      29
Jordan’s lemma      300
Kernel, Fejer      22 31
Kernel, Fourier integral      18 30 280
Kernel, Fourier series      44
Kharkevich, A. A.      145
Knopp, K.      283
Kolmogorov, A.      227
Kupfmiiller, K.      94
Laguerre polynomials      203 236
Laguerre polynomials, error correction with      236
Laguerre polynomials, expansion in      203
Landow, H. T.      67
Laplace transform      169—191
Laplace transform, analyticity of      170
Laplace transform, bilateral      187—191
Laplace transform, bilateral, of even functions      190
Laplace transform, branch points      182—185
Laplace transform, evaluation of inverse      176—185
Laplace transform, finitely many poles      176—179
Laplace transform, infinitely many poles      179
Laplace transform, inversion of      175
Laplace transform, periodic functions      181
Laplace transform, region of existence      170
Laplace transform, relationship with Fourier transform      172—175
Laplace transform, unilateral      169—187
Laplace, asymptotic method of      302
Laplace, bilateral      188
Laplace, unilateral      175 (see also Laplace transform)
Lattice densities      224
Lee, Y. W.      240 (see also Wiener-Lee transforms)
Lighthill, M. J.      269
Limit theorem      (see Central-limit theorem)
Limits, generalized      277—281
Line integral      290
Line power spectra      250
Line spectra      42—47
Line spectra, autocorrelation with      249
Linear phase causal systems      106—108
Linear phase filters      95—106
Linear phase signals, duration of      64
Linear systems      82
Linear systems, causal      85
Linear systems, output of      82
Linear systems, time-invariant      83
Linearity      14 82
Lommel’s Bessel formula      115
low-pass filters      (see Filters)
Lukacs, E.      224
Markuvitz, N.      302
Mean      18
Mean for pulse train      230
Mean, evaluation of      226
Minimization of signal duration      63
Minimization, RMS      33
Minimum-phase-shift functions      204—212
Minimum-phase-shift functions, Hilbert transforms      206—209
Modulated signals      (see Input modulated)
Modulation in spectral analysis      150
Modulation, frequency      165
Moment theorem      16—18
Moments      16
Moments, evaluation of      226
Monotonic response conditions      90
Multivalued functions      287 299
Multivalued functions, inverse transform of      182—185
Murakami, T.      105
Noise, thermal      266
Numerical techniques      53—61
Operator, linear      82
Optimum, all-pass filter      163
Optimum, input      73
Output      81
Output of linear systems      82
Overshoot      90
Page, C. H.      149
Paley — Wiener condition      215—217
Parseval’s formula      27
Parseval’s formula for causal functions      194
Partial sum      46
Periodic input to linear systems      86
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